An equivalent line element approach for free surface flow through two-dimensional rock mass including fracture networks

Abstract

In this paper, an equivalent line element method is established to analyze seepage problems with free surface through two-dimensional rock mass, including fracture networks. Low-permeablity rock matrix is characterized by the line elements as well as the high-permeablity fracture networks. Unlike the conventional equivalent continuum model, water flow in a rock mass is restricted to the line elements, and the equivalent hydraulic conductivity is determined according to Darcy's law and flux equivalence principle. As a result, uniform expressions of governing equations and boundary conditions are formulated, and the corresponding numerical procedure is developed by introducing the local coordinate and continuous Heaviside function. Satisfactory agreements with the existing test and numerical data verify this proposed line element method. The numerical solutions on the fractured slope indicate that the geological features of fractures have a substantial effect on locating the free surface. In addition, the proposed line element method can efficiently achieve accurate results with less computing time, iteration, and storage.